Question

A vector \(\overset{⃗}{A}\) when added to the sum of the vectors \((\hat{i}-2\hat{j}+2\hat{k})\) and \((-2\hat{i}+\hat{j}-\hat{k})\) gives a unit vector along Y axis. The magnitude of vector \(\overset{⃗}{A}\) is

• A. \(\sqrt{3}\)
• B. \(\sqrt{6}\)
• C. \(\sqrt{8}\)
• D. \(\sqrt{10}\)

Hint:

Subtract the sum of the two vectors from j.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Vector addition works by components. We want \(\vec A+\vec S=\hat j\) where \(\vec S\) is the sum of the two given vectors.

Step 2: Find the sum:
\[ \vec S=(\hat i-2\hat j+2\hat k)+(-2\hat i+\hat j-\hat k)=-\hat i-\hat j+\hat k \]

Step 3: Find A:
\[ \vec A=\hat j-\vec S=\hat j+\hat i+\hat j-\hat k=\hat i+2\hat j-\hat k \]

Step 4: Magnitude:
\[ |\vec A|=\sqrt{1+4+1}=\sqrt6 \]

Step 5: Choose:
Option (B).

Final Answer:
The magnitude is sqrt 6. \[ \boxed{\sqrt6} \]